IAC-08-A3.3.A1

IAC-08-A3.3.A1 MISSION AND NAVIGATION DESIGN FOR THE 2009 MARS SCIENCE LABORATORY MISSION Louis A. D’Amario Principal Member Engineering Staff Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California (USA) 91109 [email protected]

NASA’s Mars Science Laboratory mission will launch the next mobile science laboratory to Mars in the fall of 2009 with arrival at Mars occurring in the summer of 2010. A heat shield, parachute, and rocket-powered descent stage, including a sky crane, will be used to land the rover safely on the surface of Mars. The direction of the atmospheric entry vehicle lift vector will be controlled by a hypersonic entry guidance algorithm to compensate for entry trajectory errors and counteract atmospheric and aerodynamic dispersions. The key challenges for mission design are (1) develop a launch/arrival strategy that provides communications coverage during the Entry, Descent, and Landing phase either from an X-band direct-to-Earth link or from a Ultra High Frequency link to the Mars Reconnaissance Orbiter for landing latitudes between 30 deg North and 30 deg South, while satisfying mission constraints on Earth departure energy and Mars atmospheric entry speed, and (2) generate Earth-departure targets for the Atlas V-541 launch vehicle for the specified launch/arrival strategy. The launch/arrival strategy employs a 30-day baseline launch period and a 27-day extended launch period with varying arrival dates at Mars. The key challenges for navigation design are (1) deliver the spacecraft to the atmospheric entry interface point (Mars radius of 3522.2 km) with an inertial entry flight path angle error of ±0.20 deg (3σ), (2) provide knowledge of the entry state vector accurate to ±2.8 km (3σ) in position and ±2.0 m/s (3σ) in velocity for initializing the entry guidance algorithm, and (3) ensure a 99% probability of successful delivery at Mars with respect to available cruise stage propellant. Orbit determination is accomplished via ground processing of multiple complimentary radiometric data types: Doppler, range, and Delta-Differential One-way Ranging (a Very Long Baseline Interferometry measurement). The navigation strategy makes use of up to five interplanetary trajectory correction maneuvers to achieve entry targeting requirements. The requirements for cruise propellant usage and atmospheric entry targeting and knowledge are met with ample margins.

through MRO and ODY and direct-to-Earth (DTE) are INTRODUCTION significant drivers for mission design. The Mars Science Laboratory (MSL) mission will Following brief overviews of the mission and deliver a mobile science laboratory rover to the surface spacecraft in the next two sections, the remainder of the of Mars during the 2009 Mars launch opportunity. The paper will address mission and navigation design overall scientific goal of the mission is to explore and requirements and results. quantitatively assess a local region on Mars’ surface as a potential habitat for life, past or present. The MSL MISSION spacecraft will be launched in September-November 2009 from the Eastern Test Range at Cape Canaveral Launch Air Force Station in Florida on an Atlas V 541 launch The MSL spacecraft is scheduled to be launched vehicle and will arrive at Mars in July-September 2010. during the 2009 launch opportunity to Mars. The launch * The flight system consists of an Earth-Mars cruise vehicle is an Atlas V 541 consisting of a liquid oxygen stage and atmospheric entry vehicle. The entry vehicle / kerosene Common Core Booster (CCB) first stage and consists of a heatshield, backshell, descent stage a liquid oxygen / liquid hydrogen Centaur upper stage. (including sky crane), and the rover. The rover carries a The first Centaur burn establishes the 165 km x suite of 10 science instruments within the categories of 287 km, 28.9 deg inclination parking orbit, and the remote sensing, in-situ, analytical, and environmental second Centaur burn injects the spacecraft onto the (Ref. 1). The rover is powered by a Multi-Mission interplanetary transfer trajectory. The baseline 30-day Radioisotope Thermoelectric Generator (MMRTG). launch period with MRO and DTE EDL coverage During the critical ~6 min Entry, Descent, and extends from 15 September through 14 October 2009. Landing (EDL) phase, the entry system will transmit An extended launch period of up to 27 additional telemetry to the Mars Reconnaissance Orbiter (MRO) launch days extends from 15 October through and the Mars Odyssey Orbiter (ODY), both of which will be flying overhead, and also directly to Earth. The * For the Atlas nomenclature, "5" denotes five strap-on requirements for EDL telecom coverage via relay solid rocket boosters, "4" denotes a 4 m payload fairing, and "1" denotes a single-engine Centaur upper stage. 1 IAC-08-A3.3.A1

10 November 2009. The launch window on any given aimpoint, where the entry interface point is defined to day during the launch period has a duration of up to be at a Mars radius of 3522.2 km. The TCM profile is 120 min, depending on launch vehicle performance and shown in Table 1. In addition, periodic attitude the required injection energy. The launch vehicle maintenance turns are performed to provide adequate injection targets are specified as hyperbolic injection power and telecom margins, and checkouts and energy per unit mass (C3), declination of the launch calibrations of various spacecraft systems are carried asymptote (DLA), and right ascension of the launch out. The spacecraft is spin-stabilized at 2 rpm during asymptote (RLA) at the targeting interface point (TIP), cruise. defined as 5 min after spacecraft separation from the The final 45 days prior to arrival at Mars are Centaur. The injected spacecraft mass is ~4100 kg, referred to as the approach phase. During approach, the 2 2 corresponding to a maximum C3 of ~19.4 km /s . The amount of navigation tracking data increases 2 2 maximum required C3 is 17.1 km /s for the baseline launch period and 17.3 km2/s2 for the extended launch TCM Location* Description period. Excess launch vehicle performance determines TCM-1 L + 15 days Correct injection errors; remove part of the duration of the daily launch window. injection bias required for planetary protection. TCM-2 L + 120 days Correct TCM-1 errors; remove part of injection Interplanetary Cruise bias required for planetary protection. A plot of the interplanetary trajectory for the open of TCM-3 E - 60 days Correct TCM-2 errors; target to desired atmospheric entry aimpoint. the launch period is shown in Figure 1 (Ref. 2). The TCM-4 E - 8 days Correct TCM-3 errors. duration of interplanetary cruise is ~10 months. The TCM-5 E - 2 days Correct TCM-4 errors. Earth range at arrival is between 1.88 and 2.17 AU, TCM-5X E - 1 day Contingency maneuver for failure to execute depending on launch date. Detailed interplanetary TCM-5. trajectory characteristics can also be found in Ref. 2. TCM-6 E - 7 hrs Contingency maneuver: final opportunity to During interplanetary cruise, up to six Trajectory correct entry aimpoint. Correction Maneuvers (TCMs) are performed to control *Time measured from Launch (L) or Entry (E). the trajectory and adjust the atmospheric entry Table 1: TCM Profile.

Figure 1: Interplanetary Trajectory for Launch on 15 September 2009.

2 IAC-08-A3.3.A1 significantly, and spacecraft activities are focused on Deep Space Network (DSN) and via relay through approach navigation, specifically TCMs 4 and 5 (and MRO and ODY using a UHF link from MSL to the TCMs 5X or 6, if necessary), as well as preparations for orbiters. EDL coverage is also possible via relay EDL, which include initializing the onboard EDL flight through the Mars Express MEX) orbiter, although this software with the latest estimate of the atmospheric option is not currently part of the baseline mission plan. entry state vector. Figure 2 shows the locations of the seven current MSL candidate landing sites, along with the landing Entry, Descent, and Landing (EDL) sites for the Viking, Mars Pathfinder, and Mars MSL is the first Mars mission to employ a guided Exploration Rover (MER) missions. Note that all the (as opposed to ballistic) hypersonic entry in order to † MSL candidate landing sites are within a latitude range reduce landing dispersions . Prior to atmospheric entry, from 30N to 30S. As this paper was being prepared, two cruise balance masses are ejected to establish a Gale Crater was added to the list of candidate landing center-of-mass offset. This causes the entry vehicle to sites, and S. Meridiani replaced the nearby N. Meridiani have a non-zero angle of attack that provides a lift landing site. The most important effect on mission and force. During the hypersonic entry period, an onboard navigation design from adding these sites is that the guidance algorithm controls the direction of the lift total range of landing longitudes is now significantly vector (by rolling or "banking" the entry vehicle) in greater. This change is an issue only with respect to the order to compensate for entry state errors and ∆V required for landing site retargeting after launch and counteract atmospheric and aerodynamic dispersions. is addressed later in this paper. This enables MSL to achieve landing dispersions of ~12 km (99%) measured radially from the target Surface landing point. The surface phase of the mission has a nominal Prior to atmospheric entry (E) a final update to the duration of one Martian year, which is 669 Sols or 687 entry state vector (if necessary) is uplinked to the Earth days. One Sol is one Martian day or 24 hrs spacecraft as late as E – 2 hrs to initialize the onboard 37 min. During this time, the rover will drive to targets guidance algorithm. About three minutes prior to cruise of interest to conduct science investigations that focus stage separation, the cruise stage Heat Rejection System on acquisition and analysis of soil samples. During (HRS) is vented. Cruise stage separation itself occurs at surface operations, communications with the rover and E – 10 min. The entry vehicle is then despun and turned data return are accomplished via a DTE link and via to the desired entry attitude, and the cruise balance relay through MRO and ODY. The science plan for the masses are ejected. Atmospheric entry is defined to mission is described in detail in Ref. 1. occur at a Mars radius of 3522.2 km (~150 km altitude). During the hypersonic deceleration period, the SPACECRAFT onboard guidance algorithm uses knowledge of entry Figure 3 shows an expanded view of the MSL flight state vector errors and sensed accelerations to apply a system, and Figure 4 shows the flight system in cruise lift force to null out entry trajectory errors and configuration. counteract atmospheric and aerodynamic dispersions to The MSL flight system consists of an interplanetary fly to the target landing point. At ~E + 4 min at a speed cruise stage and an atmospheric entry vehicle, which is of about Mach 2.0 (450 m/s) and an altitude of ~10 km, comprised of the heatshield, backshell, descent stage the supersonic parachute is deployed, and shortly (including sky crane) and rover. The mass allocation for thereafter, the heatshield is separated. At ~E + 5 min at the entire flight system, including propellant, is a (mostly vertical) speed of ~100 m/s and an altitude of 4100 kg. During interplanetary cruise, the spacecraft is ~1.9 km, the descent stage, carrying the rover, is spin-stabilized at a nominal spin rate of 2 rpm. During separated from the backshell. The descent stage fires its the EDL phase, the entry vehicle is three-axis rocket motors to slow to a vertical speed of ~0.75 m/s at controlled. an altitude of ~20 m. The 900 kg rover is then deployed The cruise stage includes solar panels, the from the descent stage and lowered to the surface using propulsion system, which includes two propellant tanks a bridle mechanism referred to as the "sky crane". and two thruster clusters, the Attitude Control System Touchdown occurs at ~E + 6 min. The descent stage (ACS), which includes a star scanner, Inertial then cuts the bridle and executes a "flyaway" maneuver Measurement Unit (IMU), and Sun sensors, and two to impact the surface at a safe distance from the rover. antennas for X-band communications with Earth: a During EDL, communications coverage is provided Low Gain Antenna (LGA) and a Medium Gain Antenna via a direct-to-Earth (DTE) X-band link to the NASA (MGA). Cruise Stage Propulsion System † The Viking landers used a simple open-loop guidance The cruise stage propulsion system (based on MER scheme solely to maintain constant lift throughout EDL. design) consists of two propellant tanks, feed lines, a 3 IAC-08-A3.3.A1

Figure 2: Candidate MSL Landing Sites.

Figure 3: MSL Flight System – Expanded View. propellant filter, two latch valves, and eight ~5 N The thruster clusters are diametrically opposed and thrusters in two clusters of four thrusters each. The located in a plane normal to the Z-axis along a line thrusters are used for spin-rate control, attitude control, rotated 45 deg from the X axis toward the Y axis. Two and TCMs during cruise. The total usable propellant of the thrusters in each cluster ("axial" thrusters) are load is 70 kg. 4 IAC-08-A3.3.A1

coherent with the uplink. The following X-band antennas are used (see Figure 5): • One cruise stage MGA for interplanetary cruise • One parachute-cone-mounted LGA (PLGA) for interplanetary cruise and part of EDL • One backshell-mounted tilted LGA (TLGA) for EDL • A HGA and LGA pair on the Rover for surface operations Two redundant UHF transceivers in the rover support the following antennas (see Figure 5): • One parachute-cone-mounted UHF antenna (PUHF) for EDL. • One descent stage antenna (DUHF) for EDL • One rover-mounted UHF antenna (RUHF) for Figure 4: MSL Flight System – Cruise Configuration. surface operations

canted 40 deg toward the +Z and –Z directions. The other two thrusters in each cluster ("lateral" thrusters) are canted 40 deg away from the line connecting the two thruster clusters in a plane normal to the Z-axis. An axial burn imparts ∆V in the +Z or –Z direction and is accomplished by firing pairs of axial thrusters continuously for a specified time. A lateral burn imparts ∆V in a direction approximately normal to the Z-axis and is accomplished by firing all four thrusters in each cluster for 5 s (60 deg burn arc) at the appropriate orientation during each spacecraft revolution, thereby providing two 5 s lateral "pulses" per revolution). Spacecraft attitude maneuvers (turns) and spin-rate control are accomplished by pulse-mode firing of coupled thruster pairs. Nominally, there is no ∆V imparted to the spacecraft from thruster firings for Figure 5: Cruise Stage and Backshell Antennas. spacecraft turns. Thruster misalignments and thrust imbalances, however, can cause a small residual ∆V. REQUIREMENTS Therefore, an ACS/NAV characterization (consisting of The key driving requirements for mission and a pre-determined sequence of spacecraft turns) is navigation design are listed below. performed following TCM-1 to characterize the level of residual ∆V, which is an important error source Launch/Arrival Strategy and EDL Coverage modeled in the orbit determination process. • The launch period shall be at least 24 consecutive The Isp values for axial and lateral burns for TCMs days beginning on 15 September 2009 with a are 212.4 s and 221.8 s. These are average values to launch window duration of at least 30 min. reflect blowdown effects during interplanetary cruise, • The launch/arrival strategy shall allow for pre- and they have also been adjusted to account for thruster launch selection of EDL coverage via either an X- plume impingement losses of 6% for axial burns and band DTE link or a UHF link to an orbiting asset 1% for lateral burns. from atmospheric entry through landing plus one Telecom System minute. The launch/arrival strategy shall accommodate The MSL telecommunications subsystem uses • landing site latitudes between 30N and 30S. X-band for direct-to-Earth (DTE) communications The atmosphere-relative entry speed shall be during all mission phases and a UHF system during • between 5.3 km/s and 5.6 km/s. EDL and also during the surface mission for relay communications through the MRO and ODY orbiters. Launch Trajectory Design The X-band system provides both X-band uplink • Launch shall occur during daylight. and downlink. Downlink can be coherent or non-

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• The time from launch to eclipse exit or spacecraft Mars arrival date. The upper limit for entry speed (5.6 separation, whichever is later, shall be less than km/s) is dictated by the capability of the thermal 65 min. protection system used for the heatshield. The arrival date determines the season on Mars at arrival (measured Planetary Protection by a quantity called Ls‡), which has a large effect on • Launch vehicle injection targets shall be biased atmospheric density and the probability of dust storms. away from Mars to ensure that the probability of Both of these factors affect the maximum achievable Mars impact by the launch vehicle upper stage is -4 landing site altitude and the number of candidate less than 1.0 x 10 . landing sites. • The cruise TCM strategy shall ensure that the EDL communications coverage, either via a DTE probability of non-nominal impact of Mars due to link or via a relay through MRO, depends heavily on spacecraft failure during cruise is less than Mars arrival geometry and EDL trajectory geometry, -2 1.0 x 10 . which are functions of launch date, arrival date, and TCM ΔV and Propellant landing site latitude. EDL trajectory geometry is also a function of the inertial entry flight path angle (EFPA), • The 99% probability value for propellant required for TCMs and attitude/spin maintenance shall be which is selected based on EDL performance less than the available propellant. considerations. The nominal EFPA value is –15.5 deg, with a range of possible values between –14.0 deg and • The design for cruise TCMs shall be constrained to –15.5 deg. The sensitivity of EDL coverage to EFPA allow continuous X-band communications during must be taken into account when designing the all maneuvers. launch/arrival strategy. Atmospheric Entry Delivery/Knowledge Accuracies EDL coverage through MRO is heavily dependent • The entry vehicle shall be delivered to the specified on the orientation of MRO’s orbit. MRO is in a low- atmospheric entry conditions with an inertial entry altitude, sun-synchronous, frozen orbit with the flight path angle (EFPA) error less than ±0.20 deg ascending node nominally at a Local Mean Solar Time (3σ). (LMST) of 3:00 PM. • The EDL flight software shall be initialized with a The factors mentioned above result in the following state vector at an epoch at E – 9 min with list of requirements, constraints, and assumptions for accuracies of 2.8 km (3σ) in position and 2.0 m/s determining the launch/arrival strategy: 2 2 (3σ) in velocity. • C3 < 19.4 km /s . • Atmosphere-relative entry speed < 5.6 km/s. MISSION DESIGN • Ls at arrival < ~125 deg. The topics addressed in this section are • Provide DTE EDL coverage from separation to launch/arrival strategy, launch period characteristics, entry for landing latitudes between 30N and 30S. EDL coverage characteristics, and launch trajectory • Provide MRO and DTE EDL coverage from entry characteristics. to landing plus one minute for landing latitudes between 30N and 30S. Launch/Arrival Strategy • MRO antenna angle (angle between MSL anti- Requirements, Constraints, and Assumptions velocity vector and direction to MRO) < 120 deg The launch/arrival strategy consists of selection of between entry and landing + 1 min. the launch period, defined as the set of contiguous • DTE antenna angle (angle between MSL anti- launch dates that provide opportunities for injection velocity vector and direction to Earth) < 75 deg onto interplanetary transfer trajectories to Mars, and an between entry and landing + 1 min. arrival date for each launch date, such that all mission • Elevation of MRO or Earth > 10 deg at landing and requirements and constraints are met (or nearly met). landing plus + 1 min. The primary considerations for the launch/arrival • MSL must not be occulted by Mars as seen from strategy are launch vehicle performance, spacecraft MRO between entry and landing + 1 min mass, constraints caused by the EDL systems design, ‡ requirements for EDL communications coverage, and Ls is the longitude of the Sun as viewed from Mars the range of landing latitudes. measured eastward from the vernal equinox of Mars. Ls Launch vehicle performance and spacecraft mass is effectively a measure of the position of Mars in its together determine the maximum achievable launch orbit. Ls = 0 deg is the start of northern spring (southern fall), Ls = 90 deg is the start of northern energy (C3). The EDL systems design levies constraints directly summer (southern winter), Ls = 180 deg is the start of on atmosphere-relative entry speed and indirectly on northern fall (southern spring), and Ls = 270 deg is the start of northern winter (southern summer). 6 IAC-08-A3.3.A1

• Nominal EFPA is –15.5 deg (inertial) 30S, relative entry speed is 150 to 250 m/s lower than • MRO ascending node is nominally at 3:00 PM inertial entry speed.) Ls values are displayed along the (LMST). right side of the figure. The 30-day baseline launch It should be pointed out that MRO and ODY EDL period extends from 15 September through 14 October coverage are considered significantly more valuable 2009 and uses six different arrival dates between 14 than DTE EDL coverage. The primary reason is that the July and 1 August 2010. The 27-day extended launch relay link to MRO or ODY provides a high telemetry period extends from 15 October through 10 November data rate (up to 32 kbps), whereas the DTE link 2009 and has nearly continually varying arrival dates provides only "tones" that confirm that particular events between 4 August and 5 September 2010. have completed onboard the spacecraft. The added The baseline and extended launch periods were advantage of ODY coverage is that ODY can relay data developed at two different times. Initially, there was from MSL to Earth in real time (similar to what was only a baseline launch period. The extended launch done for the Mars Phoenix lander). The launch/arrival period was added later in order to provide additional strategy has been designed to provide complete EDL launch opportunities to offer relief in the event of a coverage from MRO and ODY while accepting less several week delay in assembly and testing of the than complete DTE EDL coverage, if necessary. complex MSL spacecraft. For the design of the extended launch period, certain requirements and Launch/Arrival Strategy constraints were relaxed, and some assumptions were The resulting launch/arrival strategy is illustrated in changed (described below), in order to make it possible Figure 6, with launch date on the horizontal axis and to add a significant number of additional launch arrival date on the vertical axis. The figure shows the opportunities. baseline and extended launch periods as well as The approach used for the baseline launch period contours of C3, DLA, and inertial entry speed. (Inertial (see Figure 6) was to find an initial constant arrival date entry speed is shown, because atmosphere-relative such that on the first launch date for that arrival date, entry speed is a function of landing latitude and, to a the MRO antenna angle is at its upper limit (120 deg), lesser extent, EFPA; for latitudes between 30N and and on the last day, the entry speed reaches its upper

Figure 6: Launch/Arrival Strategy.

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limit (5.6 km/s). The arrival date is moved later in steps extended launch period, the maximum C3 occurs at the and the process is repeated. In evaluating EDL end of the launch period. Based on current Atlas V 541 coverage, it was assumed that the MRO orbit node was performance, the maximum achievable C3 for a 4100 kg fixed at 3:00 PM, and the effects on EDL coverage payload (the MSL mass allocation) is ~19.4 km2/s2. constraints of varying the landing latitude between 30N Excess launch vehicle performance is utilized to and 30S were accounted for. provide a finite-duration launch window on any given For the extended launch period, perhaps the most launch day, up to a maximum duration of 2 hrs significant change is that it was assumed that the MRO (selected to bound required launch vehicle trajectory orbit node could be moved from the nominal value of analyses). The maximum DLA magnitude for all launch 3:00 PM, and that the node could be different for days in the baseline and extended launch periods is different launch dates. The requirement for DTE EDL 17.9 deg. Therefore, the standard Atlas V parking orbit coverage was waived; however, DTE coverage does with a 28.9 deg inclination will be used. Over the range still exist. Lastly, the upper limit on Ls (~125 deg) was of landing latitudes for the candidate landing sites, the allowed to be violated. However, in order to keep Ls as atmosphere-relative entry speeds are consistently less low as possible (i.e., keep arrival dates as early as than the upper limit of 5.6 km/s. possible), the arrival dates were allowed to vary continually – i.e. a different arrival date could be EDL Coverage Characteristics selected for each launch date. Keeping Ls as low as Mean Anomaly Range for MRO or ODY possible minimizes the degradation to EDL landing For any launch date and landing site, there is a range altitude capability from adverse atmospheric conditions of mean anomalies for MRO or ODY for which EDL at later arrival dates (as described above) and the coverage constraints can be satisfied. Initially, this resulting loss of candidate landing sites. mean anomaly range is determined from the constraints The approach used for the extended launch period on antenna angle at entry and elevation at landing plus (see Figure 6) was to use launch date / arrival date one minute. Nominally, the orbiter may be phased in its combinations that essentially track along the contour orbit anywhere over this range of mean anomalies – for corresponding to an atmospheric entry speed of example, to optimize EDL coverage for a particular 5.6 km/s. In evaluating EDL coverage, the MRO orbit time period or event. However, there are two factors node was changed in a stepwise manner in order to (described below) that reduce the range of possible satisfy EDL coverage constraints, and the effects on the mean anomalies. EDL coverage constraints of varying the landing First, for certain launch days and landing site latitude between 30N and 30S were accounted for. latitudes, MSL is occulted by Mars as seen from MRO The desire to have real-time ODY EDL coverage or ODY for some period of time between entry and became an issue after both the baseline and extended landing + 1 min. When this situation occurs, the mean launch periods were designed. Thus, ODY coverage anomaly range is reduced to eliminate the occultations characteristics are constrained by the launch/arrival in order to provide uninterrupted EDL coverage from strategy developed originally for MRO coverage. entry to landing + 1 min. Secondly, the accuracy with Similar to MRO, ODY is in a low-altitude, sun- which MRO and ODY can control orbital phasing is synchronous, frozen orbit. At the time of MSL arrival at ±30 s or ~±1.6 deg for a orbit period of ~2 hr. To Mars, ODY is expected to have a descending node at account for this uncertainty, the lower and upper 3:00 PM, and this is the value used for analyzing ODY bounds of the mean anomaly range are both reduced by coverage in the baseline launch period. As for MRO, it 1.6 deg. was assumed that the ODY orbit node could be varied In some cases, either there is no resulting mean in the extended launch period. anomaly range that provides uninterrupted EDL Launch Period Characteristics coverage from entry to landing + 1 min or the mean The characteristics of the baseline and extended anomaly range is less than 3.2 deg (i.e., twice the launch periods are shown in Tables 2 and 3. The tables phasing control uncertainty). This situation occurs at include launch date, arrival date, Ls, launch vehicle the most northerly landing latitudes (i.e., Mawrth and Nili landing sites) for the last several days of the injection targets (C3, DLA, and RLA), and the atmosphere-relative entry speed at the most northerly baseline launch period. and southerly candidate landing sites, as well as at a For these launch days, an exception was made to the near-equatorial landing site (to illustrate variations with assumption that the orbit node for MRO and ODY was landing latitude). fixed at 3:00 PM, and the orbit node was moved to 2:30 PM to provide full EDL coverage. For the baseline launch period, the maximum C3 occurs at the open of the launch period, whereas for the

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Launch Vehicle Injection Targets* Atmosphere-Relative Entry Speed (km/s)

Launch Launch Arrival Ls C3 DLA RLA Mawrth Meridiani Holden Day Date Date (deg) (km2/sec2) (deg) (deg) (24.88 N) (1.48 N) (26.37 S) 1 15-Sep-2009 118.1 17.092 7.136 121.707 5.493 5.468 5.496 2 16-Sep-2009 118.1 16.737 6.675 121.526 5.499 5.475 5.503 3 17-Sep-2009 118.1 16.400 6.166 121.285 5.506 5.482 5.511 4 18-Sep-2009 118.1 16.084 5.624 120.997 5.514 5.490 5.519 14-Jul-2010 5 19-Sep-2009 118.1 15.791 5.049 120.663 5.522 5.498 5.527 6 20-Sep-2009 118.1 15.524 4.438 120.290 5.530 5.506 5.536 7 21-Sep-2009 118.1 15.283 3.786 119.881 5.539 5.516 5.545 8 22-Sep-2009 118.1 15.070 3.088 119.437 5.548 5.525 5.555 9 23-Sep-2009 120.5 14.343 5.163 119.408 5.489 5.465 5.495 10 24-Sep-2009 120.5 14.146 4.550 118.920 5.496 5.473 5.504 11 25-Sep-2009 120.5 13.973 3.890 118.403 5.505 5.482 5.513 12 26-Sep-2009 19-Jul-2010 120.5 13.826 3.177 117.858 5.514 5.491 5.522 13 27-Sep-2009 120.5 13.706 2.403 117.285 5.524 5.502 5.533 14 28-Sep-2009 120.5 13.616 1.559 116.684 5.534 5.513 5.545 15 29-Sep-2009 120.5 13.558 0.635 116.054 5.546 5.526 5.557 16 30-Sep-2009 122.0 13.085 2.057 115.769 5.510 5.489 5.521 17 01-Oct-2009 22-Jul-2010 122.0 13.046 1.139 115.103 5.521 5.501 5.533 18 02-Oct-2009 122.0 13.042 0.125 114.408 5.535 5.514 5.547 19 03-Oct-2009 123.9 12.454 2.587 114.251 5.483 5.461 5.494 20 04-Oct-2009 123.9 12.448 1.647 113.531 5.494 5.473 5.507 21 05-Oct-2009 123.9 12.476 0.599 112.781 5.507 5.487 5.521 26-Jul-2010 22 06-Oct-2009 123.9 12.543 -0.575 111.997 5.521 5.502 5.536 23 07-Oct-2009 123.9 12.658 -1.902 111.174 5.539 5.520 5.555 24 08-Oct-2009 123.9 12.833 -3.410 110.293 5.559 5.541 5.576 25 09-Oct-2009 125.4 12.300 -1.217 109.920 5.514 5.496 5.531 29-Jul-2010 26 10-Oct-2009 125.4 12.478 -2.673 108.892 5.534 5.516 5.552 27 11-Oct-2009 126.8 11.976 -0.188 108.475 5.492 5.473 5.509 28 12-Oct-2009 126.8 12.190 -1.574 107.540 5.511 5.493 5.530 01-Aug-2010 29 13-Oct-2009 126.8 12.491 -3.210 106.570 5.534 5.518 5.555 30 14-Oct-2009 126.8 12.905 -5.127 105.556 5.564 5.548 5.585

= Maximum *EME2000 coordinates at TIP for optimal launch time – i.e., middle of launch window. = Minimum Table 2: Baseline Launch Period Characteristics.

Launch Vehicle Injection Targets* Atmosphere-Relative Entry Speed (km/s)

Launch Lauch Arrival Ls C3 DLA RLA Mawrth Meridiani Holden Day Date Date (deg) (km2/sec2) (deg) (deg) (24.88 N) (1.48 N) (26.37 S) 1 15-Oct-2009 4-Aug-10 127.8 12.339 -2.194 105.268 5.517 5.500 5.546 2 16-Oct-2009 5-Aug-10 128.3 12.432 -2.370 104.486 5.519 5.501 5.548 3 17-Oct-2009 6-Aug-10 128.8 12.554 -2.555 103.707 5.521 5.504 5.551 4 18-Oct-2009 8-Aug-10 129.7 12.706 -2.755 102.937 5.523 5.507 5.554 5 19-Oct-2009 9-Aug-10 130.2 12.891 -2.974 102.182 5.527 5.511 5.558 6 20-Oct-2009 11-Aug-10 131.2 12.695 -1.154 101.714 5.501 5.484 5.531 7 21-Oct-2009 12-Aug-10 131.7 12.908 -1.299 101.009 5.504 5.488 5.535 8 22-Oct-2009 13-Aug-10 132.1 13.151 -1.470 100.329 5.509 5.493 5.541 9 23-Oct-2009 12.986 0.598 99.957 5.482 5.466 5.512 15-Aug-10 133.1 10 24-Oct-2009 13.732 -1.923 99.050 5.522 5.506 5.555 11 25-Oct-2009 16-Aug-10 133.6 14.074 -2.226 98.452 5.530 5.515 5.564 12 26-Oct-2009 17-Aug-10 134.1 14.458 -2.601 97.882 5.541 5.526 5.576 13 27-Oct-2009 19-Aug-10 135.1 14.201 0.028 97.677 5.505 5.490 5.538 14 28-Oct-2009 20-Aug-10 135.6 14.582 -0.244 97.179 5.515 5.500 5.548 15 29-Oct-2009 23-Aug-10 137.0 13.888 5.368 97.352 5.445 5.427 5.472 16 30-Oct-2009 14.204 5.484 96.945 5.449 5.431 5.476 24-Aug-10 137.5 17 31-Oct-2009 15.122 2.288 96.231 5.496 5.481 5.528 18 01-Nov-2009 25-Aug-10 138.0 15.554 2.001 95.860 5.507 5.492 5.540 19 02-Nov-2009 26-Aug-10 138.5 16.028 1.585 95.508 5.521 5.506 5.554 20 03-Nov-2009 28-Aug-10 139.5 15.634 5.716 95.607 5.471 5.454 5.499 21 04-Nov-2009 30-Aug-10 140.5 15.411 9.785 95.715 5.429 5.410 5.452 22 05-Nov-2009 31-Aug-10 141.0 15.721 10.231 95.333 5.431 5.411 5.452 23 06-Nov-2009 1-Sep-10 141.5 16.039 10.964 94.952 5.432 5.412 5.453 24 07-Nov-2009 2-Sep-10 142.0 16.382 11.849 94.789 5.432 5.412 5.451 25 08-Nov-2009 3-Sep-10 142.5 16.714 12.997 94.669 5.429 5.408 5.447 26 09-Nov-2009 4-Sep-10 143.0 17.016 14.738 94.583 5.420 5.398 5.435 27 10-Nov-2009 5-Sep-10 143.5 17.271 17.867 94.566 5.402 5.378 5.411

= Maximum *EME2000 coordinates at TIP for optimal launch time – i.e., middle of launch window. = Minimum Table 3: Extended Launch Period Characteristics.

9 IAC-08-A3.3.A1

Baseline Launch Period cannot provide this capability. Table 4 shows characteristics of MRO, ODY, and Figure 7 illustrates EDL coverage geometry for DTE EDL coverage for the baseline launch period. The MRO and ODY for a trajectory targeted to Mawrth for minimum and maximum values are with respect to launch at the open of the baseline launch period (15 variations across the launch period. Data are provided September 2009). The plot shows the incoming MSL for the Mawrth (North), Meridiani (Equatorial), and trajectory, the orbits of MRO and ODY, the landing site Holden (South) landing sites to illustrate how EDL location, the directions to Earth and Sun and the coverage characteristics vary for with landing latitude. directions from MSL to MRO and ODY. The labeled For MRO and ODY EDL coverage, the tables include positions of MSL, MRO, and ODY correspond to the mean anomaly range for orbiter phasing (see time of atmospheric entry, and the orbit nodes for MRO explanation in next section), antenna angle at entry, and ODY are at 3:00 PM. MRO is moving from south elevation at landing + 1 min, and required orbit node. to north, and ODY is moving from north to south. The The antenna angle and elevation data correspond to the end points for the orbits of MRO and ODY are at the middle of the mean anomaly range. For DTE EDL time of landing. coverage, the following data are included: EDL DTE EDL coverage for the baseline launch period visibility from separation to entry, antenna angle at (see Table 4) is always available from cruise stage entry, elevation at landing + 1 min, and percentage of separation to atmospheric entry (a hard requirement). total EDL duration that is visible. Values in red indicate However, because the launch/arrival strategy was not where full DTE coverage is not possible. designed to provide full DTE EDL for all launch days Referring to Table 4, full EDL coverage is possible and all latitudes, full DTE EDL coverage is in general from MRO for all of the baseline launch period with the possible only for launch dates toward the end of the orbit node at the nominal value of 3:00 PM, except for launch period and only for northerly landing latitudes. northerly landing latitudes for several days at the end of Otherwise, EDL coverage ends some time after entry the launch period. For days 27 through 30, the orbit when MSL is occulted by Mars as viewed from Earth. node must be at 2:30 PM in order to provide full EDL EDL coverage extends to landing, or nearly to landing, coverage. The minimum mean anomaly range is 6 deg for northerly and equatorial landing sites, but only to in the north and generally increases with deceasing approximately one minute past entry for southerly latitude. The maximum MRO antenna angle at entry is landing sites. The maximum Earth antenna angle at close to 120 deg in the north and generally decreases entry is always well below 75 deg and increases with with decreasing latitude. The minimum MRO elevation decreasing latitude. The minimum Earth elevation at at landing + 1 min is always well above 10 deg. In landing + 1 min is below 10 deg for all landing latitudes general, MRO EDL coverage characteristics improve gets progressively worse at equatorial and southerly with decreasing latitude. landing site latitudes. In general, DTE EDL coverage The EDL coverage situation is similar for ODY. The characteristics degrade with decreasing latitude, a differences are that the orbit node must be at 2:30 PM behavior that is opposite to that for MRO and ODY for all landing latitudes for one or more days at the end EDL coverage). of the launch period, and there is no definitive trend in antenna angle as a function of landing site latitude. Extended Launch Period Analyses have demonstrated that whenever MSL is in Table 5 shows characteristics of MRO, ODY, and view from ODY, Earth is also in view, so that ODY can DTE EDL coverage for the extended launch period. For provide a real-time telemetry relay during EDL. MRO MRO and ODY EDL coverage for the extended launch

Min/Max MA Range (deg) Min/Max Ant Angle at Entry (deg) Min/Max Elev at Lnd + 1m (deg) Required LMST Node (PM)* North Equatorial South North Equatorial South North Equatorial South North Equatorial South 6 10 19 109 106 88 21 28 18 3:00 (1) MRO 3:00 3:00 21 19 22 118 115 101 60 79 33 2:30 (27) 6 8 14 101 108 106 22 26 15 3:00 (1) 3:00 (1) 3:00 (1) ODY 32 30 28 117 119 120 60 51 35 2:30 (30) 2:30 (25) 2:30 (27)

Visibility from SEP to Entry? Min/Max Ant Angle at Entry (deg) Min/Max Elev at Lnd + 1m (deg) Min/Max EDL Coverage (%)**

DTE North Equatorial South North Equatorial South North Equatorial South North Equatorial South 14 26 40 7 -2 -17 83% 79% 13% Y Y Y 27 38 53 20 9 -11 100% 88% 21%

North = Mawrth (24.65 N) Equatorial = Meridiani (1.48 N) South = Holden (26.37 S) *Number in parentheses is first launch day at which node value applies. **Coverage starts at entry and ends when Mars occults MSL as seen from Earth. Table 4: Baseline Launch Period EDL Coverage Characteristics: Variations Across 30 Launch Days.

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Figure 7: EDL Coverage Geometry – Mawrth (15 September 2009 Launch). period (see Table 5), the most significant difference at landing + 1 min are very similar, with the exception from the baseline launch period is that the LMST of the that the minimum mean anomaly ranges are somewhat orbit node must be moved progressively earlier as the lower. As for the baseline launch period, ODY can launch period progresses in order to be able to provide provide a real-time telemetry relay during EDL. full EDL coverage. For developing the launch/arrival DTE EDL coverage for the extended launch period strategy, the LMST is moved earlier in steps of 30 min. (see Table 5) is significantly improved as compared to For equatorial and southerly latitudes, the steps occur the baseline launch period, because Earth visibility of later – i.e., any given LMST can be maintained for a EDL is more favorable at later arrival days. The Earth greater number of launch days. elevations at landing + 1 min are significantly higher. As compared to the baseline launch period, mean Full, or nearly full, DTE coverage is possible for the anomaly ranges, antenna angles at entry, and elevations entire extended launch period for northerly and

Min/Max MA Range (deg) Min/Max Ant Angle at Entry (deg) Min/Max Elev at Lnd + 1m (deg) Required LMST Node (PM)* North Equatorial South North Equatorial South North Equatorial South North Equatorial South 2:30 (1) 2:30 (1) 2:30 (1) 2:00 (6) 2:00 (9) 2:00 (9) 5 7 14 110 104 72 26 37 13 MRO 1:30 (14) 1:30 (15) 1:30 (15) 22 19 21 119 117 101 74 86 51 1:00 (20) 1:00 (21) 1:00 (21) 12:30 (25) 12:30 (27) 12:30 (27) 2:30 (1) 2:30 (1) 2:30 (1) 2:00 (4) 2:00 (3) 2:00 (5) 9 5 5 101 111 103 30 21 11 ODY 1:30 (10) 1:30 (10) 1:30 (13) 25 32 27 117 119 118 48 46 31 1:00 (17) 1:00 (17) 1:00 (20) 12:30 (24) 12:30 (24) 12:30 (24)

Visibility from SEP to Entry? Min/Max Ant Angle at Entry (deg) Min/Max Elev at Lnd + 1m (deg) Min/Max EDL Coverage (%)**

DTE North Equatorial South North Equatorial South North Equatorial South North Equatorial South 26 37 53 22 11 -10 100% 91% 22% Y Y Y 45 48 62 48 13 22 100% 100% 91%

North = Mawrth (24.65 N) Equatorial = Meridiani (1.48 N) South = Holden (26.37 S) *Number in parentheses is first launch day at which node value applies. **Coverage starts at entry and ends when Mars occults MSL as seen from Earth. Table 5: Extended Launch Period EDL Coverage Characteristics: Variations Across 27 Launch Days.

11 IAC-08-A3.3.A1 equatorial landing latitudes. For southerly latitudes, twilight and no later than the end of evening civil only partial EDL coverage is possible, ranging from twilight. The beginning of morning civil twilight and slightly more than one minute to nearly complete the end of evening civil twilight are defined to occur coverage. Values in red indicate where full DTE when the center of the Sun is geometrically 6 deg below coverage is not possible the horizon. Figures 8 and 9 show plots of launch time as a function of launch date for open, middle, and close Launch Trajectory Characteristics of a 2 hr launch window (maximum duration) for the The key factors for MSL launch trajectory design baseline and extended launch periods. The plots also are time of launch, time from launch to eclipse exit, and show daylight time constraints as appropriate. All DSN initial acquisition characteristics. launch times occur during daylight. Due to additional range safety requirements for a Approximately 7 min prior to launch, the MSL launch payload containing radioisotope materials, MSL spacecraft transfers to internal power. After separation launch must occur during daylight. Daylight is defined from the Centaur upper stage and exit from eclipse, the to be no earlier than the beginning of morning civil spacecraft solar arrays will provide electrical power to

Figure 8: Launch Times – Baseline Launch Period.

Figure 9: Launch Times – Extended Launch Period.

12 IAC-08-A3.3.A1 the spacecraft systems. In order not to exceed the constraint. For the extended launch period, the time spacecraft battery capacity, the time from launch to from launch to eclipse exit increases, and on days 26 eclipse exit or spacecraft separation, whichever is later, and 27, the constraint is violated either for part or all of must be less than 65 min. Because eclipse exit always the launch window. As this paper was being prepared, occurs after separation, this requirement defaults to the the MSL project has decided to implement a strategy eclipse exit time. Figures 10 and 11 show plots of time that allows the spacecraft solar arrays to charge the from launch to eclipse exit as a function of launch date battery whenever they are illuminated between parking for open, middle, close of a 2 hr launch window orbit insertion and eclipse entry in order to provide (maximum duration) for the baseline and extended adequate power margin for the end of the extended launch periods. The plots also show the 65 min launch period constraint. Missing data points for open, middle, or Initial acquisition of the spacecraft radio signal by close of the launch window indicate that no eclipse the DSN can occur after activation of the spacecraft occurs for that launch date and time. For the baseline radio transmitter (following separation from the launch period, there is considerable margin against the Centaur and eclipse exit) and after a DSN complex has

Figure 10: Time from Launch to Eclipse Exit – Baseline Launch Period.

Figure 11: Time from Launch to Eclipse Exit – Extended Launch Period.

13 IAC-08-A3.3.A1 the spacecraft in view. As noted earlier, eclipse exit • Minimize operational complexity. always occurs after spacecraft separation, so that • Minimize atmospheric entry delivery errors. transmitter turn-on occurs no earlier than eclipse exit. • Minimize total cruise propellant usage. Canberra is always the first DSN complex to have the TCMs 4, 5, and 6 occur during the approach phase, spacecraft in view, and this usually occurs after eclipse which starts at E – 45 days. These TCMs adjust the exit; however, for launches near the close of the launch trajectory to the desired atmospheric entry conditions. window for launch days toward the end of the extended TCM-5 at E – 2 days is the final entry targeting launch period, eclipse exit is after Canberra rise. A maneuver for landing site safety – i.e., TCM-5 is the ground track plot for launch on 15 September 2009 at last maneuver required to achieve the EFPA delivery open of the launch window is shown in Figure 12. accuracy requirements. TCM-6 at E – 7 hrs is the final

Figure 12: Ground Track Plot for Launch on 15 September 2009 at Open of Launch Window (GDS = Goldstone, MAD = Madrid, CAN= Canberra). opportunity to adjust the trajectory. In the event that NAVIGATION DESIGN there has been an anomaly during or after TCM-5 (or This section addresses the TCM profile, orbit TCM-5X) that causes an unwanted ∆V, or for any other determination analysis, and propulsive maneuver reason a late TCM is required, TCM-6 is the final analysis. Orbit determination analysis includes opportunity to ensure that the delivery accuracy atmospheric entry delivery and knowledge accuracies requirements are met. Although TCM-6 is a and approach navigation sensitivities. Propulsive contingency maneuver, it is being prepared for in maneuver analysis includes injection aimpoint biasing, exactly the same manner as the other approach phase non-nominal impact probability, TCM ∆V and maneuvers. propellant statistics, and landing site retargeting. The navigation tracking data cutoff time for TCMs 1 TCM Profile through 3 is 5 days prior to the TCM; for TCMs 4, 5, In order to achieve the atmospheric entry delivery and 5X, the data cutoff is 12 hours prior to the TCM; accuracy requirement for EFPA, five nominal and two for TCM-6, the data cutoff is 5 hours prior to the TCM. contingency TCMs are planned during the cruise and The data cutoffs for the final four TCMs are closer to approach phases. Table 1 lists the name, nominal execution of the TCM in order to reduce navigation execution time, and a description of the maneuver for tracking data latency, thereby improving entry delivery each TCM. The TCM locations are chosen as a accuracy. All TCMs utilize the so-called “Auto-TCM” compromise between competing requirements: behavior, similar to that developed for MER. The • Provide sufficient time between launch and TCM-1 commands to execute the TCM are part of flight for spacecraft checkout and design of TCM-1. software. The ground TCM design process determines a • Provide sufficient time between TCMs to allow for set of parameters that govern the execution of the TCM, TCM reconstruction, orbit determination, and and these parameters are uplinked to the spacecraft sequence generation for the upcoming TCM. prior to scheduled execution. The “Auto-TCM” behavior also includes logic that can detect faults and,

14 IAC-08-A3.3.A1 after recovery from the fault, resume execution of the on dynamic models to infer position, as is the case with TCM. Doppler and range. The assumed radiometric data accuracies for MSL Orbit Determination (OD) orbit determination analyses are as follows (Ref. 3): Radiometric Data Accuracy Doppler 0.1 mm/s (1σ) The baseline radiometric data types used for orbit Range 3.0 m (1σ) determination are two-way coherent Doppler, two-way ∆DOR 2.4 nrad (1σ) ranging, and Delta Differential One-way Range In addition, quasar location errors are assumed to be (∆DOR) measurements generated by the DSN X-band 1.0 nrad (1σ). tracking system. All data types are derived from a Navigation Tracking Schedule coherent radio link between the spacecraft and a The DSN 34-meter High Efficiency (HEF) subnet receiver at a DSN ground station. In the case of ∆DOR will be utilized for acquisition of Doppler, range, and measurement, a radio signal from a quasar will also be ∆DOR data for navigation. The tracking schedule used used to obtain the measurements. for orbit determination analyses is shown in Table 6. Doppler data yield a measurement of line-of-sight Doppler and range tracking coverage is continuous spacecraft range rate. During tracking passes in the for the first 30 days following launch and for the entire two-way coherent mode of operation, the DSN tracking approach phase starting at E – 45 days. ∆DOR system measures Doppler shift by accumulating the measurements start approximately 30 days after launch, cycles of the downlink carrier signal in order to determine the difference between the transmitted and received frequencies. Time Span Doppler/Range !DOR Two-way range is also a line-of-sight measurement. Launch to L + 30 days Continuous None 3 8-hr passes 1 point per The DSN ranging system constructs an estimate of the L + 30 days to E – 45 days per week week range to the spacecraft by measuring the round-trip 2 points per E – 45 days to E – 28 days Continuous light time of a radio signal between the ground station week and the spacecraft. 2 points per E – 28 days to Entry Continuous ΔDOR is a Very Long Baseline Interferometry day measurement of a spacecraft using pairs of DSN Table 6: DSN Tracking Schedule. stations (either Goldstone-Madrid or Goldstone- Canberra) and an intergalactic radio source (i.e., and the frequency increases to two points per day (with quasar). Two DSN stations simultaneously observe the alternating baselines) during the final 28 days prior to spacecraft followed by simultaneous observations of the entry. The final two ∆DOR measurements prior to the quasar. ∆DOR directly measures angular separation navigation data cutoff for a TCM design are not between the spacecraft and the quasar in the direction included for analysis purposes to account for ∆DOR of the projected baseline between the two stations. The data processing latency. ΔDOR observable is a phase delay time expressed in units of nanoseconds (ns) that is equivalent to an OD Filter Assumptions angular separation between the spacecraft and the The orbit determination analysis results presented quasar; a delay of 1 ns corresponds to an angular below are based on linear covariance analyses that separation of ~37.5 nrad. ∆DOR measurements simulate orbit determination processing with a multiple determine the spacecraft position in the plane of the batch consider-parameter filter. The baseline OD filter sky. The Goldstone-Madrid baseline (oriented East- assumptions are shown in Table 7 and discussed below. West) primarily measures the right ascension Radiometric data accuracies and the navigation component of the spacecraft position, and the tracking schedule were discussed previously. For each Goldstone-Canberra baseline (oriented Northeast- tracking pass, constant Doppler and range data biases Southwest) primarily measures the declination are estimated. component of the spacecraft position, with a substantial All TCMs contained within the data arc are also dependency on right ascension as well. ∆DOR estimated. Future TCMs occurring after the navigation measurements are generally scheduled with alternating data cutoff time are treated in one of two ways. For baselines. The ∆DOR data type complements line-of- generating entry delivery uncertainties, the TCM sight Doppler and range measurements because of its directly after the data cutoff time is "considered" in the orthogonality to those data types. Furthermore, ∆DOR filter at the a priori uncertainty, while any other future and range data provide a near-instantaneous TCMs are ignored. For a consider parameter, the error measurement of spacecraft position and thus do not rely source is included at the a priori value, but the parameter is not estimated. For generating orbit

15 IAC-08-A3.3.A1 determination covariances for propulsive maneuver accounts for shadowing of the backshell from the cruise analyses, all future TCMs are ignored, and maneuver stage as a function of solar aspect angle. Each execution errors are modeled in the maneuver analysis component has a mean specular and diffuse coefficient process. of reflectivity associated with it, and a reflectivity ACS ∆V events (i.e., residual ∆V caused by degradation schedule. Use of this high-fidelity solar spacecraft turns for attitude maintenance) that fall pressure model eliminates the need to include an error within the data arc are estimated, and future events are source for unmodeled non-gravitational accelerations in considered. Each ∆V from an ACS event is modeled the OD filter. with a three-component impulse. Other stochastically estimated parameters include The solar pressure model consists of a single flat Earth orientation parameters (pole X/Y and UT1§), plate representing the solar array and the area inside of media effects (troposphere and ionosphere), and Earth the solar array, including the launch vehicle adaptor. In and Mars ephemerides. The considered parameters are

A Priori Estimated/ Uncertainty Correlation Update Error Source Considered (1!) Time Time Comments X-Band 2-way Doppler (mm/s) – 0.1 – – Range (m) – 3 – – !DOR (ns) – 0.06 – – Equivalent to 2.4 nrad. Epoch State Position (km) Est. 1000 – – Epoch State Velocity (km/s) Est. 1 – – Solar Radiation Pressure Three-component high-fidelity model. Gr = Radial Component (%) Est. 5 7 days 1 day Correlation broken at turns. Gx = Tangential Component (%) Est. 5 7 days 1 day Gr, Gx estimated both as bias and Gy = Out-of-Plane Component (%) Est. 1 – – stochastic. Doppler Bias (mm/s) Est. 0.002 0 Per pass Range Bias (m) Est. 2 0 Per pass Based on analysis assuming one DE414 "DOR per month from MRO/ODY for Mars & Earth Ephemerides Est. – – Covariance one Earth/Mars synodic period prior to MSL arrival. Mars GM (km3/s2) Est. 2.8 x 10-4 – – From PHX. Full 2003 Station Locations (cm) Con. – – Covariance Quasar Locations (nrad) Con. 1 – – Earth Orientation Parameters Ramp from 2 days before EOP Pole X/Y (cm) Est 1 # 4 48 hrs 6 hrs delivery to EOP + 12 hr. Ramp from 6 days before EOP UT1 (cm) Est 1.7 # 15 48 hrs 6 hrs delivery to EOP + 12 hr. Ionosphere – Day/Night (cm) Est 55/15 6 hrs 1 hr S-band units. Use 6x (ionosphere) and 2x (troposphere) apsig when no actuals. Subsequent passes are Troposphere – Wet/Dry (cm) Est 1/1 6 hrs 1 hr uncorrelated. 2 mm/s before Turns occur at L + 15 days and every E – 45 days, 7 days thereafter up to E – 8 days. ACS Event !V – Per Axis (mm/s) Est. – – 1 mm/s after Uncertainties are per flight system E – 45 days requirements. Removed because of improved solar 2 – 0 – – Non-gravitational Accelerations (km/s ) radiation pressure model. TCM Execution Errors (mm/s) 8% proportional error (3!); 4 mm/s TCM-1 (L + 15 days) fixed error (3!), turn/burn maneuver. TCM-2 (L + 120 days) Magnitudes of TCM execution errors are Est. TCM-3 (E – 60 days) specific to each trajectory. 8% proportional error (3!); 4 mm/s fixed error (3!); vector mode TCM-4 (E – 8 days) maneuver. TCM-5 (E – 2 days) Table 7: Baseline Orbit Determination Filter Assumptions. addition, a cylinder model represents the launch vehicle § UT1 is the principal form of Universal Time that is adaptor and the heat rejection system, while an antenna corrected for the effect of polar motion and is model represents the backshell. The antenna model proportional to the true rotation angle of the Earth with respect to a fixed frame of reference. 16 IAC-08-A3.3.A1 quasar locations and DSN station locations, since maneuver execution errors mapped to the atmospheric tracking data does not improve estimates of these entry interface point is referred to as TCM delivery quantities. accuracy. Atmospheric entry knowledge accuracy for In addition to the baseline OD filter assumptions, a position or velocity is the OD knowledge accuracy at set of "No Margin" assumptions is also used. The “No entry (computed from the position or velocity Margin" scenario applies the following assumptions: covariance norm) based on an OD data cutoff at E – • Unlikely faults and out-of-spec performance (both 6 hrs. This section presents results for entry delivery accounted for in the baseline assumptions) do not and knowledge accuracies based on linear covariance occur. analyses that use the models and assumptions discussed • All requested Doppler and range tracking passes above. TCMs 4 and 5 during the approach phase are the are successful. key maneuvers for targeting to the desired entry • All requested ∆DOR measurements are successful, interface conditions. The entry interface targets are and the data processing latency is consistent with EFPA, B-plane angle, and entry time (see Figure 13). performance for past missions. Targeting a specific B-plane angle and entry time The difference in navigation performance between corresponds to targeting a specific latitude and the “No Margin” and baseline assumptions quantifies longitude on the surface. Given a desired landing site the level of margin included in the navigation design. target and EFPA value, the values for B-plane angle The “No Margin” OD filter assumptions have the and entry time are determined from an EDL trajectory following changes with respect to the baseline simulation that varies the entry conditions to achieve assumptions listed in Table 7 (all values 1σ unless the desired landing site latitude and longitude. The otherwise noted): EFPA is selected based on results of EDL Monte Carlo • Doppler accuracy = 0.05 mm/s. simulations to evaluate the performance of the entry • ∆DOR accuracy = 0.04 ns (1.6 nrad). guidance algorithm. For MSL, the nominal EFPA is • Gr (radial) and Gx (tangential) errors for solar -15.5 deg, although a shallower (i.e., less negative) radiation pressure = 2%. value may be used. • Range bias = 1 m. EFPA error is proportional to the error in the • Pole X/Y errors = 1 cm (constant value). magnitude of the B-vector that depends on the B-plane • Upper limit on UT1 error = 7.5 cm. angle and the orientation of the B-plane error ellipse. • Fixed maneuver execution error = 2 mm/s (3σ). Figure 14 illustrates the dependence of EFPA error on B-plane angle for a fixed error ellipse orientation. If the Approach Navigation Accuracies semi-major axis of the error ellipse lies along the The combination of orbit determination errors and B-vector (Ellipse 1), the EFPA error is maximized. If

Figure 13: Entry Interface Point, B-plane, and B-plane Angle.

17 IAC-08-A3.3.A1

the baseline launch period cases, the landing latitudes correspond to the northern and southern limits of possible latitude range plus an equatorial case. For the extended launch period, it was decided to use actual candidate landing sites with extreme northerly and southerly latitudes.

Launch Launch Arrival Landing Period Date Date Latitudes / Sites 15-Sep-2009 14-Jul-2009 Baseline 30N, 0, 30S 14-Oct-2009 1-Aug-2010 15-Oct-2009 4-Aug-2010 Nili (21.0N), Extended 10-Nov-2009 5-Sep-2010 Holden (26.4S) Table 8: Approach Navigation Analysis Cases.

The entry delivery and knowledge accuracy results Figure 14: Dependence of EFPA Error on B-plane for the above cases are shown in Table 9. The TCM-4 Angle. and TCM-5 delivery errors assume a navigation data the semi-minor axis of the error ellipse lies along the cutoff 12 hrs prior to the TCM. The entry knowledge B-vector (Ellipse 2), the EFPA error is minimized. errors assume a data cutoff at E – 6 hrs. Ellipse 3 illustrates an intermediate case. In a similar The values for the TCM-4 EFPA delivery error are fashion, assuming the B-plane angle is fixed, the B- very similar for the different cases, with the exception vector magnitude error will vary as the orientation of of the case at close of the extended launch period for the error ellipse changes. For the cases that have been the Nili landing site. The TCM-5 EFPA delivery errors analyzed for MSL, the size, shape, and orientation of exhibit the same behavior. The EFPA delivery the B-plane error ellipse does not vary for a given requirement is met, or nearly met, at TCM-4 and TCM, so that B-plane angle is a more important factor always met at TCM-5 with ample margin. With “No for determining EFPA error. Margin” assumptions, EFPA errors improve EFPA error is also a function of the targeted EFPA. significantly, such that the delivery requirement is Steeper (i.e., more negative) EFPA values produce always met at TCM-4. These results indicate that it is smaller EFPA errors; likewise, shallower (i.e., less unlikely that TCM-5 will be required. negative) EFPA values produce larger EFPA errors. At For entry state knowledge, the requirements for the nominal EFPA of –15.5 deg, a change in EFPA of position and velocity accuracy are always met with +1.0 deg causes EFPA error to increase by less than significant margin. Entry knowledge errors are smallest 0.01 deg, which is a small effect. at northerly latitudes and increase as landing latitude The cases selected for analyzing entry delivery and moves south. As expected, “No Margin” assumptions knowledge curacies are shown in Table 8. The launch significantly improve entry knowledge. date / arrival date combinations correspond to open and Figure 15 shows 3σ B-plane error ellipses for the close of the baseline and extended launch periods. For case at open of the baseline launch period targeted to a

3! EFPA Delivery Error (deg) 3! Entry State Knowledge Error* Launch Launch Arrival Landing TCM-4 TCM-5 Position (km) Velocity (m/s) Period Date Date Latitude / Site Baseline No Margin Baseline No Margin Baseline No Margin Baseline No Margin 30N ±0.22 ±0.16 ±0.09 ±0.05 1.1 0.9 0.9 0.7 15-Sep-2009 14-Jul-2010 0 ±0.21 ±0.16 ±0.08 ±0.05 1.7 1.3 1.2 0.9 30S ±0.21 ±0.16 ±0.08 ±0.05 1.9 1.4 1.3 1.0 Baseline 30N ±0.19 ±0.11 ±0.08 ±0.04 1.3 1.0 1.0 0.7 14-Oct-2009 1-Aug-2010 0 ±0.20 ±0.11 ±0.08 ±0.05 1.9 1.4 1.4 1.0 30S ±0.21 ±0.12 ±0.08 ±0.05 2.1 1.6 1.5 1.1 Nili (21.0N) ±0.19 ±0.12 ±0.07 ±0.04 1.4 1.0 1.0 0.8 15-Oct-2009 4-Aug-2010 Holden (26.4S) ±0.21 ±0.14 ±0.08 ±0.05 2.0 1.6 1.4 1.1 Extended Nili (21.0N) ±0.15 ±0.10 ±0.04 ±0.02 1.1 0.9 0.9 0.7 10-Nov-2009 5-Sep-2010 Holden (26.4S) ±0.19 ±0.13 ±0.07 ±0.05 2.1 1.7 1.6 1.2 Requirement ±0.20 2.8 2.0 *Arbitrarily defined as three times the position or velocity covariance norm. Table 9: Entry Delivery and Knowledge Accuracy Results.

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Figure 15: B-plane Error Ellipses: Launch on 15 September 2009, 30N Latitude.

30N landing latitude. Ellipses are included for TCM-4 where multiple assumptions have been changed. For and TCM-5 delivery uncertainties and for entry each of the sensitivity studies discussed in this section, knowledge uncertainty. The TCM-4 error ellipse only one parameter is changed with respect to the slightly exceeds the ±0.20 deg EFPA delivery baseline assumptions to understand the effect of only requirement. Note that the TCM-4 error ellipse is nearly that parameter. Each of the error sources for the OD circular, which is typical for all cases studied. This filter (see Table 7) is changed to an “improved” value explains why TCM-4 EFPA errors are insensitive to and a “degraded” value. In general, the baseline value is landing latitude (see Table 9) for all but one case. The halved and doubled to produce the improved and TCM-5 error ellipse is more eccentric, but the effect is degraded values. not large, and TCM-5 EFPA errors are also insensitive Due to space limitations, the quantitative results for to landing latitude. There are two entry knowledge all the sensitivity studies cannot be included here. The ellipses that are virtually identical. One assumes sensitivity results are summarized in Table 10 and TCM-4 is the final maneuver (a likely scenario); the discussed below. other assumes TCM-5 is the final maneuver. Whether TCM-4 EFPA delivery accuracy is most sensitive to or not TCM-5 is performed has little effect on entry TCM-4 execution errors and ACS event ∆V. Doubling knowledge accuracy. The entry knowledge ellipses any one of these error sources causes the ±0.20 deg show that between TCM-5 and the E – 6 hr navigation (3σ) EFPA delivery requirement (marginally met at data cutoff for entry knowledge, the uncertainties have TCM-4) to be violated. For TCM-5, the EFPA delivery been reduced mostly in the EFPA direction (i.e., along accuracy is most sensitive to TCM 4 and 5 execution the B-vector). errors and ∆DOR accuracy and latency. However, the EFPA delivery requirement can still be met even if any Approach Navigation Sensitivities of these error sources is doubled. Entry knowledge In order to understand the effects on entry delivery accuracy is most sensitive to Earth-Mars ephemeris and knowledge accuracies of changes in OD filter errors, ∆DOR accuracy and latency, and quasar location assumptions and navigation data assumptions, a series errors. Doubling any of these error sources does not of sensitivity studies have been performed. Navigation cause the entry knowledge requirement to be violated. data assumptions include data types, data quantity, and, In general, if all ∆DOR data or all range data are for entry knowledge errors, the navigation data cutoff deleted, TCM 4 and 5 EFPA delivery accuracies and time. The “No Margin” results discussed in the entry knowledge accuracies degrade to the point that previous section represent one type of sensitivity study

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Baseline Sensitivity Type Value Change Results Largest sensitivities for TCM-4 delivery: • TCM-4 execution error • ACS event !V Largest sensitivities for TCM-5 delivery: OD Filter Halved or • TCM 4 & 5 execution errors Table 7 Assumptions Doubled • !DOR accuracy & latency Largest sensitivities for entry knowledge: • Earth-Mars ephemeris errors • !DOR accuracy & latency • Quasar location errors • TCM-4 delivery requirement violated if all !DOR and/or all range data removed. Doppler, Data Types / Delete data • TCM-5 delivery requirement violated if all Range, & Quantity type(s) !DOR data removed. !DOR • Entry knowledge requirement violated if all !DOR and/or all range data are removed. Position uncertainties (with TCM-5): 2.5 - 4.0 km for baseline launch period 3.0 - 7.0 km for extended launch period No TCM-5 ! ~20% improvement. Entry Knowledge "No Margin" ! ~30% improvement. E – 6 hrs E – 33 hrs Data Cutoff Time Velocity uncertainties (with TCM-5): 1.5 - 3.0 m/s for baseline launch period 3.0 - 7.0 m/s for extended launch period No TCM-5 ! ~15% improvement. "No Margin" ! ~30% improvement. Table 10: Approach Navigation Sensitivity Study Results. their respective requirements are violated. The requirements can still be achieved, however, if only a Propulsive Maneuver Analysis small amount of range data (a few hours per day during Maneuver Strategy the approach phase) and partial ∆DOR data (only East- TCMs are required to compensate for launch vehicle West or only Northeast-Southwest baselines) are injection errors, injection aimpoint biasing for planetary available. protection, orbit determination errors, and maneuver The navigation data cutoff for the final estimate of execution errors and to accommodate landing site the entry state vector to be uplinked to the spacecraft retargeting after launch. Landing site retargeting is for use by the onboard entry guidance algorithm is discussed in more detail in a subsequent section. TCMs nominally at E – 6 hrs. It would be desirable to move are inherently statistical in nature (i.e., non- the data cutoff earlier to allow more processing time for deterministic), since they are required to correct for orbit determination and to uplink a sufficiently accurate trajectory dispersions from various error sources. estimate of the entry state significantly earlier relative However, TCMs may have a deterministic component. to atmospheric entry. The next earlier opportunity to The maneuver strategy described in this section uplink the entry state to the spacecraft corresponds to a attempts to minimize total cruise statistical ∆V and data cutoff time at E – 33 hrs. Unfortunately, with this propellant usage while satisfying all mission data cutoff time, the entry knowledge requirements requirements and spacecraft constraints. (2.8 km and 2.0 m/s, both 3σ) are generally violated, The goal of the maneuver strategy is to minimize the except for certain cases for the baseline launch period. total required cruise propellant for TCMs and However, with the earlier data cutoff time, the entry spacecraft attitude/spin control while satisfying various knowledge accuracy can be improved significantly mission constraints, such as launch vehicle and either by assuming TCM-5 is not executed (very likely) spacecraft planetary protection requirements. The high- or by taking advantage of the "No Margin" results. level maneuver strategy used for the results presented in Some combination of these two effects should enable this section assumes that for the design of the reference the entry knowledge requirement to be met. interplanetary trajectory TCMs 1 and 2 may have The sensitivity results demonstrate that, in general, deterministic components in order to minimize the ∆V entry delivery and knowledge accuracies are fairly cost to remove Mars aimpoint biasing for planetary robust to degradations to OD filter assumptions and protection and to retarget the landing site. For statistical navigation data assumptions. Monte Carlo maneuver analyses, the total ∆V for TCMs

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1, 2, and 3 are optimized to minimize the total ∆V cost 50 deg in the presence of dispersions and to satisfy the -Z^ spacecraft non-nominal impact probability requirement.

Maneuver Analysis Assumptions 40 deg The assumptions used for propulsive maneuver analyses reported in this paper are as follows: • The TCM profile is as given in Table 1. • A spacecraft turn is permitted at TCM-1; all subsequent TCMs must be performed at the nominal cruise attitude**. • The total spacecraft mass at injection onto the interplanetary trajectory is 4100 kg. • The spacecraft is spin-stabilized during cruise at a Figure 16: Thruster Cant Angles. nominal spin rate of 2 rpm. • The total cruise stage usable propellant load for arbitrary direction in order to execute TCM-1. The TCMs and attitude/spin control during combination of these pointing constraints creates a interplanetary cruise is 70 kg. region within which the spacecraft –Z axis can be • The nominal thrust level of the cruise stage pointed. In the discussion that follows, this region is thrusters at initial propellant tank pressure is 4.7 N. referred to as the “allowable pointing region”. Figure 17 shows the plane defined by the Earthline • The effective Isp values for axial and lateral maneuvers are 212.4 s and 221.8 s, respectively. and Sunline directions, the regions within 75 deg of the (These values reflect blowdown effects during Earthline direction (shaded blue) and within 50 deg of cruise have been adjusted to account for thruster the Sunline direction (shaded red), the allowable plume impingement losses of 6% for axial burns pointing region (shaded magenta), and maneuver and 1% for lateral burns.) implementation modes for several example ∆V vectors. • The lateral ∆V direction is at an angle of 100.6 deg TA indicates turn and axial burn, TL indicates turn and from the spacecraft –Z axis. (This results from a lateral burn, and TAL indicates turn and vector mode propulsion system constraint that the lateral ∆V burn. A vector mode burn accomplishes the desired ∆V vector must be directed through the spacecraft vector by executing axial and lateral burn components center of mass in order not to cause spacecraft that add to the desired ∆V vector. Performing a vector attitude perturbations during TCMs.) mode burn without a turn is also an option. • The spacecraft –Z axis off-Earth and off-Sun For example ΔV1, the desired ∆V vector is most angles at TCM-1 must be less than 75 deg and efficiently accomplished by a turn and axial burn in the § 50 deg . (These constraints ensure that there will be –Z direction. For example ΔV2, the maneuver is most a communications link with Earth and adequate efficiently accomplished by a turn and lateral burn. For spacecraft power margin at TCM-1.) this case, the –Z axis is pointed as indicated by the gray • Thruster burn penalties caused by thruster cant vector in the allowable pointing region. (For simplicity, angles (see Figure 16) are 55.6% for axial burns the lateral ∆V direction is shown perpendicular to the and 30.5% for lateral burns; the finite burn arc axial ∆V direction.) For example ΔV3, the maneuver is penalty for lateral burns (60 deg burn arc; 5 s burn) most efficiently accomplished by a turn and vector is 4.7%§. mode burn. For this case, the –Z axis is pointed as indicated by the black dashed line labeled “Axial ΔV” Propulsive Maneuver Implementation Modes on the border of the allowable pointing region. In order to provide communications with Earth and For statistical maneuver analyses, two options adequate spacecraft power margin during propulsive referred to the “MarsVZ” option and “No-Turn Vector” maneuvers, the spacecraft –Z axis must be pointed option are considered. The MarsVZ option allows all within a specified angle relative to both the Earth and maneuver implementation modes described above in Sun directions. For example, at TCM-1, the angle order to achieve the desired ∆V vector most efficiently: between the –Z axis and the Earthline direction must be turn and axial burn (TA), turn and lateral burn (TL), less than 75 deg, and the angle between the –Z axis and and turn and vector mode burn (TAL). The No-Turn the Sunline direction must be less than 50 deg. Vector option assumes no spacecraft turn is permitted. Consequently, the spacecraft is not free to turn to any The spacecraft –Z axis is assumed to be pointed along the nominal cruise attitude direction (which by design

satisfies the Earth and Sun pointing constraints). ** These assumptions are discussed in more detail in the next section. 21 IAC-08-A3.3.A1

Figure 17: Propulsive Maneuver Implementation Modes.

For TCM-1, the MarsVZ option is used. At the time The overall ∆V penalty for lateral burns is thus 36.7% of TCM-1, the spacecraft is still using the cruise LGA (1.305 x 1.047 – 1), which is significantly lower than for communications with Earth. The beam width of the for axial burns (55.6%). From a ∆V penalty standpoint, LGA permits large off-Earth angles. However, TCMs 2 lateral burns are more efficient. In addition, because the through 5 are performed after the switch to the cruise effective Isp of the lateral thrusters is higher, they are MGA. The boresight of the MGA must be pointed even more efficient in terms of propellant mass within ~9 deg of Earth at all times. For this reason, and consumed. This means a lateral burn is often the for operational simplicity, the No-Turn Vector option is preferred mode. used for all TCMs subsequent to TCM-1. The physical orientations of the cruise stage Maneuver Execution Accuracy thrusters (see Figure 16) cause ∆V penalties for axial The accuracy with which a given propulsive and lateral burns. The axial thrusters have a 50 deg cant maneuver can be executed is a function of the angle with respect to the axial direction (spacecraft Z propulsion system behavior and the attitude control axis), and the lateral thrusters have a 40 deg cant angle system that maintains the pointing of the spacecraft with respect to the lateral direction (assumed for during thruster firings. Propulsion system error sources simplicity to be normal to the axial direction). The cant include thruster misalignments and thrust variations angle ∆V penalties for axial and lateral burns are: between thrusters. Maneuver execution errors are specified in terms of ∆V magnitude and pointing errors, Axial ∆V penalty = 1/cos(50°) – 1 = 55.6% each of which has a component proportional to the Lateral ∆V penalty = 1/cos(40°) – 1 = 30.5% commanded ∆V magnitude (proportional errors) and a component independent of ∆V magnitude ("fixed" Lateral burns also have a finite burn arc penalty. For errors). lateral burns, the thrusters are fired for 5 s over a burn The maneuver execution accuracies for the MSL arc of θ = 60 deg. The finite burn arc penalty is: cruise stage are listed in Table 11. TCM-1 has a higher proportional error, because TCM-1 is the first TCM. Lateral burn arc penalty = (θ/2)/sin((θ/2) – 1 = 4.7% The proportional error for subsequent TCMs is lower, because thruster performance will have been calibrated based on results from TCM-1 and from thruster firings

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for spacecraft turns and calibration activities. The required to achieve the desired landing point. The more maneuver execution accuracies in Table 11 are conservative value of 0.7 x 10-4 is used to allow for incorporated into statistical maneuver analyses. slight inaccuracies from using linearized methods for determining the impact probability. Error Source TCM-1 TCMs 2-5 Note that the method described above provides a Proportional magnitude error (3!) 8% 5% biased injection aimpoint that minimizes TCM-1 Proportional pointing error, per axis (3!) 80 mrad 50 mrad deterministic ∆V. This aimpoint does not minimize Fixed magnitude error (3!) 4 mm/s 4 mm/s total cruise statistical ∆V when known error sources, Fixed pointing error, per axis (3!) 4 mm/s 4 mm/s such as launch vehicle injection errors, orbit Table 11: Maneuver Execution Accuracies. determination errors, and maneuver execution errors, are included. However, given that the process of finding the biased injection aimpoint that minimizes total cruise Injection Aimpoint Biasing statistical ∆V would involve a laborious iterative One of the planetary protection requirements listed process, and that ∆V and propellant margins are not earlier in this paper states that after injection, the currently a significant concern (as will be shown in the probability of the launch vehicle upper stage (i.e., the results that follow), the biased aimpoint has been Centaur) impacting Mars must be less than 1.0 x 10-4. In determined to minimize deterministic TCM-1 ∆V for order to meet this requirement, the injection aimpoint the analyses contained herein. must be biased away from Mars. The process to find a Figure 18 shows, for an example case, the 1σ biased injection aimpoint that satisfies the above injection error ellipse, the 10-4 Mars impact probability planetary protection requirement and minimizes the ellipse, and the biased injection aimpoint and associated subsequent ΔV required to remove the bias determines 1σ error ellipse in the Mars B-plane. The size, shape, -4 the point on the 0.7 x 10 Mars impact probability and orientation 1σ injection error and 10-4 Mars impact ellipse (due to launch vehicle injection errors) in the probability ellipses depend on injection errors and Mars B-plane, that minimizes the TCM-1 deterministic trajectory dynamics. The biased injection aimpoint for ∆V. This ellipse is centered on the B-plane aimpoint the spacecraft is chosen such that the Mars impact that corresponds to the atmospheric entry conditions probability is ~0.7 x 10-4.

Figure 18: 1σ Injection Error Ellipse, 10-4 Mars Impact Probability Ellipse, Biased Injection Aimpoint and Associated 1σ Error Ellipse in Mars B-plane for Launch on 15 September 2009.

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Following the injection burn, the Centaur upper failure rate. For TCM-5 (nominally the final maneuver), stage experiences ∆Vs caused by spacecraft separation the non-nominal impact probability is defined as an at injection + 3.7 min, the Contamination and Collision impact resulting from a trajectory with an EFPA that Avoidance Maneuver (CCAM) at injection + ~17 min violates the ±0.20 deg EFPA delivery requirement, and to move the Centaur away from the spacecraft and the associated Q(i+1) value is 1.0. The total non- preclude contamination of the spacecraft during the nominal impact probability is computed as: subsequent blowdown maneuver, and finally the blowdown maneuver to deplete residual Centaur Σ{ Π [1-Q(i)] x P(i) x Q(i+1) } propellant. The effect on the Centaur trajectory of these ∆Vs must be taken into account in satisfying the The Π [1-Q(i)] term above represents the probability Centaur impact probability requirement. that all preceding maneuvers have been completed The attitudes for spacecraft separation, CCAM, and successfully and has a value very close to, but slightly blowdown determine the direction of the ∆Vs smaller than, 1.0. However, this term has not experienced by the Centaur for these events. The conventionally been included in non-nominal impact separation attitude has been determined to ensure that probability calculations, so that the slightly more the spacecraft has adequate telecom and power margins conservative value computed from Σ [ P(i) x Q(i+1) ] is for the first 15 days following injection. This attitude is used. The difference in the resulting cumulative non- such that the separation ∆V always moves the Centaur nominal impact probability is on the order of 10-5, and, aimpoint away from Mars and decreases the Centaur therefore, does not significantly affect the results. Mars impact probability. The attitudes for CCAM and Preliminary calculations have shown that, if all blowdown may be specified, within launch vehicle TCMs are targeted directly to the desired atmospheric attitude constraint, such the ∆Vs from these events will entry conditions at Mars, the total non-nominal impact also move the Centaur aimpoint away from Mars. A probability exceeds the 1.0 x 10-2 requirement. The single CCAM attitude has been found that has the largest contributions are from TCMs 1, 2, and 3. desired characteristics, and the blowdown maneuver Consequently, the aimpoints for TCMs 1 and 2 are uses this same attitude. biased away from Mars (according to empirically determined rules) to reduce their contributions to the Non-nominal Impact Probability total non-nominal impact probability. For TCM-1, the The second planetary protection requirement states B-magnitude of the aimpoint is constrained to be that the cumulative probability of non-nominal impact ~200 km further from Mars than the desired aimpoint. of Mars due to spacecraft failure during the cruise For TCM-2, the B-magnitude is constrained to be phase must be less than 1.0 x 10-2. A non-nominal further from Mars than the desired aimpoint by an impact is an impact that could result in the break-up of amount corresponding to the semi-major axis the spacecraft and release of terrestrial contaminants on dimension of the TCM-2 delivery error ellipse Mars. For TCMs 1 through 4, the non-nominal impact (typically ~700 km). For statistical maneuver analyses, probability is defined as the probability of impact after the biased aimpoints for TCMs 1 and 2 are optimized, the TCM, P(i), multiplied by the probability that the within the constraints described above, to minimize the subsequent maneuver does not occur, Q(i+1). The total ΔV cost of TCMs 1 through 3. Q(i+1) values are supplied by the planetary protection Table 12 shows an example of a non-nominal office at JPL and are based on an assumed spacecraft impact probability calculation, along with the details of

Event P(i) Q(i+1) P(i) x Q(i+1) ! [ P(i) x Q(i+1) ] Launch 0.00E+00 2.93E-06 0.00E+00 0.00E+00 Injection 7.00E-05 1.05E-03 7.36E-08 7.36E-08 TCM-1 1.31E-04 3.16E-03 4.15E-07 4.89E-07 TCM-2 2.61E-02 1.27E-02 3.32E-04 3.32E-04 TCM-3 1.00E+00 3.61E-03 3.61E-03 3.94E-03 TCM-4 1.00E+00 4.16E-04 4.16E-04 4.36E-03 TCM-5 2.79E-16 1.00E+00 2.79E-16 4.36E-03 P(i) = non-nominal impact probability following TCM(i) = total impact probability (with 100 km atmosphere) for TCMs 1 through 4 = impact probability for EFPA violating ±0.20 deg delivery requirement for TCM-5 Q(i+1) = probability that TCM(i+1) does not occur, given that TCM(i) has occurred TCM-1 aimpoint constraint " |B| > target + 200 km (i.e., outside impact radius) TCM-2 aimpoint constraint " |B| > target + 700 km (1 SMAA of delivery ellipse) Table 12: Non-nominal Impact Probability for Launch on 15 September 2009.

24 IAC-08-A3.3.A1 the TCM-1 and TCM-2 aimpoint constraints. For this Landing Site Retargeting case, the total non-nominal impact probability is Landing site retargeting after launch is also taken 4.36 x 10-3, with the largest contribution from TCM-3. into account for statistical maneuver analyses. Landing site retargeting refers to retargeting the interplanetary TCM ΔV and Propellant Statistics trajectory to an atmospheric entry aimpoint that Statistical Maneuver Analysis Process corresponds to a different landing site than was used to The statistical maneuver analysis process determines develop the final launch vehicle injection targets. The the TCM ΔV and cruise propellant (including ACS final launch vehicle injection targets (C3, DLA, and propellant) required at the 99% probability level for RLA) are delivered to the launch services provider at TCMs and spacecraft attitude/spin control. The TCM approximately 5 months prior to launch. The work to ∆V and cruise propellant statistics are generated by develop the target specification document starts at performing 5000-sample Monte-Carlo analyses that about 10 months prior to launch, at which time simulate dispersions caused by launch vehicle injection selection of the final landing site will not yet have errors, orbit determination errors, and maneuver occurred. Therefore, the final launch vehicle injection execution errors; these analyses also take into account targets are determined from interplanetary trajectories injection and TCM aimpoint biasing for planetary targeted to what is referred to as the "central landing protection and landing site retargeting after launch. For site" (defined below). Following launch, the trajectory each Monte Carlo sample, the total ∆V for TCMs 1, 2, is retargeted to the final selected landing site, starting at and 3 is minimized by varying the (biased) aimpoints TCM-1 and using the TCM-1/2/3 optimization process for TCMs 2 and 3 within the constraints imposed to described above. satisfy the requirement for spacecraft non-nominal The central landing site is defined as the landing impact probability. TCM-3 targets to the final desired point with a latitude and longitude each of which is atmospheric entry aimpoint. Figure 19 shows, for the approximately at the midpoint of the extremes of same example case as was used for Figure 18, the latitude and longitude for all candidate landing sites. statistical mean aimpoints and 1s delivery error ellipses This minimizes the maximum latitude and longitude for TCMs 1 and 2. The point labeled "Target Aimpoint" changes required for retargeting the landing site after corresponds to the desired atmospheric entry aimpoint. launch. The ∆ V cost for landing site retargeting is

Figure 19: Statistical Mean Aimpoints and 1σ Delivery Error Ellipses for TCMs 1 and 2 for Launch on 15 September 2009.

25 IAC-08-A3.3.A1 driven by longitude changes, which require changing correspond to open and close of the baseline and the arrival time at Mars; in contrast, the ∆V cost for extended launch periods. For each case the landing site latitude changes is significantly less. Prior to the is retargeted after launch from the central landing site at addition of the Gale landing site, the minimum and 0.0N/20.0E to the Nili and Holden landing sites. Prior maximum latitudes for all candidate landing sites (see to the addition of Gale, these two sites represented the Figure 2) were 26.4S (Holden) and 24.7N (Mawrth). largest combined latitude and longitude changes with Similarly, the minimum and maximum longitudes were respect to the above central landing site. -34.9E (Holden) and 74.5E (Nili). The central landing site was chosen to be at 0.0N / 20.0E, with a maximum Launch Launch Arrival required longitude change of ~55 deg. The statistical Period Date Date Landing Sites* TCM ∆V and propellant results presented below 15-Sep-2009 14-Jul-2009 Baseline Nili assume this central landing site. With the Gale landing 14-Oct-2009 1-Aug-2010 (21.0N, 74.5E) site (4.5S, 137.4E) included, the central landing site 15-Oct-2009 4-Aug-2010 Holden Extended would be at 0.0N / 50.0E, resulting in a maximum 10-Nov-2009 5-Sep-2010 (26.4S, 325.1E) required longitude change of ~87 deg. The propellant *Central landing site: 0.0N, 20.0E. required to achieve this larger longitude change is also presented below. Table 13: Statistical Maneuver Analysis Cases. Propellant Calculations Table 14 presents a summary of the statistical In order to calculate statistical cruise propellant maneuver analysis results for the case at open of the mass, first the "ideal" ∆Vs for each TCM are computed baseline launch period for the Holden landing site, for each Monte Carlo sample as described above. The along with key assumptions and constraints. The table ideal ∆V represents the desired inertial velocity change includes, for each TCM, the deterministic ∆V (for the and does not reflect ∆V penalties caused by propulsion reference trajectory) and the mean, 1σ, and 99% values system inefficiencies, such as thruster cant angles and for ideal and implemented ∆V and propellant mass. The the lateral finite burn arc, or ∆V penalties for particular total propellant required for TCMs and ACS at the 99% maneuver implementation modes (e.g., vector mode probability level is 37.8 kg, of which 24.5 kg are for maneuvers) that are required because of spacecraft –Z TCMs and ~13.3 kg are for ACS. With respect to the axis pointing constraints. The ideal ∆Vs are then 70- kg cruise stage propellant load, the propellant converted to "implemented" ∆Vs, which account for all margin is a healthy 32.3 kg (46%). Note that these the ∆V penalties mentioned above. The implemented ∆Vs are then used to calculate the total cruise results are for a central landing site at 0.0N / 20.0E. Several facts are worth noting with respect to the propellant mass (via the rocket equation) for each data in Table 14. The largest part of the deterministic Monte Carlo sample. ∆V to remove the launch vehicle injection bias and Total cruise propellant includes ACS propellant retarget the landing site occurs at TCM-2. This usage in addition to TCM propellant. ACS propellant is indicates that it is more efficient from a celestial required for the activities: mechanics standpoint to accomplish these corrections at • Spin rate correction after launch vehicle separation. TCM-2. If the entire deterministic ∆V were forced to • Spacecraft turns for TCM-1. occur at TCM-1, the total deterministic ∆V would be • Attitude/spin maintenance during and after TCMs. significantly higher. Although TCM-2 has by far the • ACS/NAV characterization turns. larger deterministic ∆V, the 99% values for ideal ∆V, • Attitude maintenance turns. implemented ∆V, and propellant mass are roughly • Turns to calibrate the descent stage IMU. equivalent for TCMs 1 and 2. This indicates that it is • Fault protection response turns. more efficient to correct many launch vehicle injection Mean and 1σ values for the above activities have dispersions at TCM-1. The growth factor from ideal ∆V been supplied by the flight system team. The propellant to implemented ∆V is ~1.7, and the conversion factor for TCM-1 turns is a function of the TCM-1 turn angle from implemented ∆V to propellant mass is statistics from the Monte Carlo maneuver analysis. The ~1.9 kg/m/s, which is directly a function of ∆V, 99% value for ACS propellant usage is typically spacecraft mass, and I . Overall, 1 m/s of ideal ∆V 13-14 kg and does not vary significantly as a function sp translates into ~3.3 kg of propellant mass. of interplanetary trajectory (i.e., launch and arrival For the other cases in Table 13, the detailed results dates). The final step is to combine the TCM and ACS show similar behavior to that shown in Table 14, propellant statistics to produce total cruise propellant although the numerical values are different. The results statistics. for all eight cases are summarized in Table 15. All Statistical Maneuver Analysis Results cases have adequate propellant margin for the landing Table 13 lists the eight cases for which statistical sites analyzed, assuming a central landing site at maneuver analyses have been performed. These cases 26 IAC-08-A3.3.A1

Det. "V Ideal "V (m/s) Implemented "V (m/s) Propellant Mass (kg) TCM Location (m/s) µ 1! "V99 µ 1! "V99 µ 1! "M99 TCM-1 L + 15 d 0.31 1.27 0.96 4.05 2.16 1.62 6.92 4.17 3.14 13.32 TCM-2 L + 120 d 2.46 2.44 0.56 3.83 4.12 1.02 6.97 7.82 1.95 13.22 TCM-3 E - 60 d 0 0.29 0.14 0.72 0.55 0.27 1.35 1.06 0.51 2.61 TCM-4 E - 8 d 0 0.08 0.04 0.21 0.15 0.08 0.42 0.29 0.16 0.81 TCM-5 E - 2 d 0 0.02 0.01 0.04 0.03 0.02 0.08 0.06 0.03 0.15 Total 2.77 4.10 1.12 7.36 7.02 1.98 12.71 13.40 3.83 24.51 Assumptions and constraints: • Thruster cant angles = 50 deg (axial), 40 deg (lateral). • Injection covariance matrix from July 2007 launch trajectory • Thrust per thruster = 4.7 N. analysis. • Isp = 212.4 s (axial), 221.8 s (lateral). • Planetary protection biasing for injection, TCM-1 & TCM-2. • Angle between –Z axis and lateral burn direction = 100.6 deg. • TCM-1: MarsVZ mode; TCMs 2-5: vector mode. • Lateral burn arc = 60 deg (5 s). • TCM-1 turn constraints: 75 deg off-Earth, 50 deg off-Sun. • Central landing site = 0.0N / 20.0E. • Injected mass = 4100 k 99% TCM Propellant, kg = 24.5 ACS Propellant, kg = 13.3 99% TCM + ACS Propellant, kg = 37.8 Cruise Propellant Load, kg = 70.0 Propellant Margin, kg = 32.2 (46%) Table 14: Statistical Maneuver Analysis Results: Holden Landing Site, 15 September 2009 Launch, Central Landing Site at 0.0N / 20.0E.

99% !V (m/s) 99% Propellant Mass (kg, %) Launch Arrival Landing Det. !V** Imple- Date Date Site* (m/s) Ideal mented TCM TCM + ACS Margin*** Holden 2.8 7.4 12.7 24.5 37.8 32.2 46% 9/15/09 7/14/10 Nili 3.3 7.5 13.0 25.1 38.3 31.7 45% Holden 4.0 7.5 12.3 23.5 37.5 32.5 46% 10/14/09 8/1/10 Nili 4.4 8.0 12.7 24.6 38.5 31.5 45% Holden 3.8 7.3 11.9 22.5 36.4 33.6 48% 10/15/09 8/4/10 Nili 4.2 8.2 13.3 25.8 39.8 30.2 43% Holden 4.1 6.8 11.1 21.3 35.7 34.3 49% 11/10/09 9/5/10 Nili 4.2 7.4 12.0 23.2 37.8 32.2 46% *Central landing site: 0.0N / 20.0E. **TCM-1 + TCM-2. ***With respect to 70 kg propellant load. Table 15: Summary of Statistical Maneuver Analysis Results.

0.0N / 20.0E. Note that the total variation in 99% cruise ∆V and propellant costs with Gale included, a special propellant mass and propellant margin across the study was carried out. baseline and extended launch periods is only ~2 kg for Statistical maneuver analyses have been performed both the Holden and Nili landing sites. Also, the values to determine the 99% cruise propellant mass (TCM plus for Holden and Nili are very similar, primarily due to ACS) for longitude changes up to ±180 deg. This the fact that the longitude changes for retargeting from longitude range was chosen to encompass the ~87 deg the central landing site to these landing sites are nearly longitude change required for Gale and also to identical (~55 deg). determine the maximum possible longitude change in The results discussed above assume a central the event that some new candidate landing site was landing site at 0.0N / 20.0E and post-launch retargeting added in the future. In addition, large latitude changes to the Holden and Nili landing sites. This is appropriate were included, so that any synergistic effect from a if the Gale landing site (added after the analyses combination of large latitude and longitude changes discussed above had been completed) is not considered. would be uncovered. These analyses were done for the With Gale included, the central landing site should be at open of the baseline launch period. 0.0N / 50.0E, and the maximum required longitude The results are presented in Table 16 In order to change increases to ~87 deg. In order to understand the reduce the time and effort to generate the results, the old central landing site (0.0N / 20.0E) was used for the

27 IAC-08-A3.3.A1

Latitude / Longitude 26.4S / 200.0E 26.4S / 260.0E 26.4S / 325.1E 0.0N / 20.0E 21.0N / 74.5E 21.0N / 140.0E 21.0N / 200.0E !Lat / !Lon (deg) -26.4 / -180.0 -26.4 / -120.0 -26.4 / -54.9 0 / 0 +21.0 / +54.5 +21.0 / +120.0 +21.0 / +180.0 Entry Date/Time (ET) 7/14/10 21:44 7/14/10 17:37 7/14/10 13:16 7/14/10 9:11 7/14/10 5:35 7/14/10 1:06 7/13/10 21:00

! Entry Time 12:32 8:25 4:04 0 -3:36 -8:05 -12:11 Det. !V (m/s)* 6.5 4.4 2.8 – 3.3 5.8 8.0

99% Prop. Mass (kg) 58.2 46.0 37.8 – 38.3 47.8 56.8 Prop. Margin (kg)** 11.8 24.0 32.2 – 31.7 22.2 13.2 *TCM-1 + TCM-2. **With respect to 70 kg propellant load. Table 16: Cruise Propellant Margin as Function of Longitude Change for Launch on 15 September 2009.

reference for retargeting; however, the results should attitude control, entry guidance, and powered descent apply for any central landing site. For each case, the guidance and control. Flight hardware device models following parameters are tabulated: atmospheric entry include the entry vehicle ACS thrusters and the descent date/time, change in entry time, deterministic ∆V, 99% stage IMU. cruise propellant mass (TCM plus ACS), and propellant The two primary functions for EDL trajectory margin. Note the values for longitude change and analysis are reference trajectory design to determine the propellant margin, which are tabulated in red. These atmospheric entry aimpoint to achieve a specified results indicate that for a 70 kg propellant load, any landing point and Monte Carlo analyses to evaluate longitude within ±180 deg of the central landing site, EDL performance, including landing dispersions. for latitudes between about 30N and 30S, can be achieved with retargeting the trajectory after launch. In Reference Trajectory Design other words, any point on the surface of Mars with a The atmospheric entry aimpoint used as the target latitude between about 30N and 30S is accessible. for interplanetary cruise TCMs consists of inertial The two cases in Table 16 for longitude changes of EFPA, entry B-plane angle, and entry time, where the –54.9 deg and +54.5 deg correspond to retargeting to entry interface point is defined to be at a Mars radius of the Holden and Nili landing sites from the old central 3522.2 km. The nominal value for EFPA is –15.5 deg; landing site. The ∆V/propellant results for these two however, the EFPA may be adjusted to optimize entry cases are identical to those in Table 15. For the new guidance performance. central landing site, the longitude change required for The design of the reference EDL trajectory involves Holden is –84.9 deg; similarly, the longitude change for determination of the entry B-plane and time that Gale is +87.4 deg. These landing sites represent the achieve a desired landing point (i.e., latitude and new bounding cases in terms of maximum required longitude) on the surface of Mars, given a specified longitude change and maximum propellant usage. By EFPA and entry guidance profile (specifically, the bank interpolating the data in Table 16, the propellant angle profile used to orient the lift vector to null out margins for retargeting to Holden and Gale are entry trajectory errors and compensate for atmospheric estimated to be 28.5 kg and 27.0 kg. These margins are and aerodynamic dispersions.) Entry B-plane angle and slightly smaller than those in Table 15 because of the entry time both affect the latitude and longitude of the larger longitude changes. landing point. The entry B-plane angle and time are varied interactively to converge the latitude and EDL TRAJECTORY ANALYSIS longitude to the desired values. The reference trajectory EDL trajectory analysis utilizes software that design may also include an outer-loop to adjust the simulates the EDL trajectory starting at atmospheric EFPA to provide desirable characteristics for the entry entry (or earlier, if necessary) and extending though guidance profile. landing. This trajectory simulation includes all the key Reference EDL trajectories are needed for EDL events, such as atmospheric deceleration, interplanetary trajectory design (including generation of hypersonic entry guidance, supersonic parachute launch vehicle injection targets), approach navigation deployment, powered descent, and landing. The analyses (for entry delivery and knowledge accuracies), simulation can be performed either in three-degree-of- and cruise statistical maneuver analyses. freedom (3DOF) mode or 6DOF mode and includes EDL guidance, navigation, and control (GNC) flight Monte Carlo Analyses software as well as flight hardware device models. EDL Monte Carlo analyses are performed to GNC flight software functionalities include state evaluate EDL system performance in the presence of estimation (position, velocity, attitude, attitude rate), various error sources. The metrics for EDL system

28 IAC-08-A3.3.A1 performance include landing accuracy (i.e., distance Figure 20 shows an example plot of landing from target landing point), aerodynamic heating rate dispersions from an EDL Monte Carlo analysis. These and total heating load, atmospheric entry deceleration results are for the Mawrth landing site for launch at level, various parachute deployment parameters open of the baseline launch period. DSENDS and (including altitude), and heatshield Mach number. The POST are the names of EDL trajectory simulation error sources include atmospheric entry delivery and software tools used at JPL and the NASA Langley knowledge errors, entry attitude errors, aerodynamic Research Center. The 99.87% high range error at dispersions, and atmospheric dispersions. The entry landing (i.e., distance from target) is 11.9 km††. At delivery and knowledge errors are each represented by 99.0% probability, this value is 9.8 km. As compared to a set of 8000 dispersed entry state vectors generated MER, the distribution of landing dispersions for MSL is from an approach navigation covariance analysis as more nearly circular and less Gaussian, and the errors described earlier in this paper. are smaller. The semi-major axis of the MER landing The flight software entry guidance algorithm uses dispersion ellipses (i.e., along the downtrack direction) knowledge of the entry state vector (uplinked from the was typically 30-35 km at the 99% probability level. ground), the spacecraft attitude at entry (determined The more nearly circular shape and non-Gaussian onboard), and sensed accelerations (from the IMU) to characteristics of the MSL landing dispersions as well "fly out" errors in the entry conditions, compensate for as the improved accuracy, all derive from the use of aerodynamic and atmospheric dispersions, and land at hypersonic entry guidance.

Figure 20: Landing Dispersions from EDL Monte Carlo Analysis 08-MAW02-01: Mawrth Landing Site, 15 September 2009 Launch. the desired point on the surface. This is accomplished by controlling the lift vector of the entry vehicle to †† EDL Monte Carlo analyses conventionally report adjust crosstrack and downtrack range from the target. values at the 99.87% probability level, which is the 3σ probability for a one-dimensional normal distribution. 29 IAC-08-A3.3.A1

CONCLUSIONS This paper has described the strategies for mission and navigation design and presented analysis results to demonstrate that all mission and navigation design requirements can be achieved. The launch/arrival strategy provides EDL communications coverage via an X-band DTE link and a UHF link to MRO and ODY for landing latitudes between 30N and 30S. The launch/arrival strategy employs a 30-day baseline launch period and a 27-day extended launch period with varying arrival dates at Mars. The LMST node for the orbit of MRO or ODY must be moved progressively earlier in the extended launch period in order to provide EDL coverage. The navigation strategy makes use of complimentary radiometric data types (Doppler, range, and ∆DOR) for orbit determination and five planned interplanetary TCMs to achieve atmospheric entry delivery and knowledge requirements. A central landing site is used for generation of launch vehicle injection targets, and the trajectory is retargeted to the desired landing site after launch. Statistical maneuver analyses indicate that ample margins exist for required cruise propellant (for TCMs and ACS) with respect to the usable propellant load. ACKNOWLEDGEMENTS The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The author would like to acknowledge the members of the MSL Mission Design and Navigation Team, who performed the analyses that are reported on in this paper: Fernando Abilleira, Darren Baird, Dan Burkhart, Julie Kangas, Tomas Martin-Mur, Sumita Nandi, and Mau Wong. The author also acknowledges the contributions of the MSL EDL systems and GNC teams. Stacy Weinstein, Tim McElrath, and Mike Watkins served as reviewers for this paper and provided useful comments. REFERENCES

1 Mars Science Laboratory Mission Plan, JPL D-27162, MSL-272-0211, 10 September 2007. 2 Mars Science Laboratory Interplanetary Trajectory Characteristics Document, JPL D-27210, 31 July 2008. 3 Mars Science Laboratory Navigation Plan, JPL D-33445, 7 March 2008.

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